Need Help Solving (adding eight numbers from 1,2,3,4,5,6,7,8,9,10,11,12 to get 49)

[smithasn]

I am not sure if I Am wording this correctly but here goes:

If i have the numbers, 1,2,3,4,5,6,7,8,9,10,11,12

And i can only use 8 of the above numbers when added to get the number 49

Numbers can repeat.

How many combinations are there that will equal 49

What are those number combinations of 8 numbers that equal 49?

I could not find a calculator to show these?

 

[stapel]

I am not sure if I Am wording this correctly but here goes:

If i have the numbers, 1,2,3,4,5,6,7,8,9,10,11,12

And i can only use 8 of the above numbers when added to get the number 49

Numbers can repeat.

How many combinations are there that will equal 49

What are those number combinations of 8 numbers that equal 49?

I could not find a calculator to show these?

I would doubt that there *is* a calculator for this. Instead, you'll have to work it yourself.

For instance, can you get to 49 by adding 1's eight times? No. What if you added 1's five times? Could you add other numbers in to get 49?

And so forth.

Eliz.

 

[BigBeachBanana]

I am not sure if I Am wording this correctly but here goes:

If i have the numbers, 1,2,3,4,5,6,7,8,9,10,11,12

And i can only use 8 of the above numbers when added to get the number 49

Numbers can repeat.

How many combinations are there that will equal 49

What are those number combinations of 8 numbers that equal 49?

I could not find a calculator to show these?

Combination Sum Calculator

 

[smithasn]

I would doubt that there *is* a calculator for this. Instead, you'll have to work it yourself.

For instance, can you get to 49 by adding 1's eight times? No. What if you added 1's five times? Could you add other numbers in to get 49?

And so forth.

Eliz.

Sorry I worded it incorrectly please see the following, I met ADD
If i have the numbers, 1,2,3,4,5,6,7,8,9,10,11,12

And i can only use 8 of the above numbers when added to get the number 49

Numbers can repeat.

How many combinations are there that will equal 49

What are those number combinations of 8 numbers when added that equal 49?

I could not find a calculator/calculation to show these?

I m looking for combinations ----How many when added gets you 49

10,7,5,7,7,4,1,8 -----these eight when added get 49
so does 10,9,8,7,6,5,3,1

So how many more of these these Adding combinations are there?

 

[smithasn]

Please advise if I am wording this problem correctly and what are the solution (is there some equation for combinations )/ Answers:


SET of numbers 1,2,3,4,5,6,7,8,9,10,11,12 months of the year.

Within the exact time frame of 10 years I MUST choose a number of the month each year that when combined with other months (their number placement in the calendaer) over those ten years in total add up to 49.

--------------------------
Constriants:
I must to use exactly eight of the above numbers when added together produce the number 49 over those ten years

Numbers can be used over (repeated) but MUST be eight in total over those ten years.

Questions:

1) How many combinations are there that will equal 49



2) What are those number combinations of eight numbers when added together that equal 49? over thos ten years.
---------------------------


I'm looking for how many combinations there are

Eaxmple:

10,7,5,7,7,4,1,8 ----- these eight when added get 49

10,9,8,7,6,5,3,1 also adds up to 49

 

[Steven G]

Come on, you need to try.
BigBeachBanana even gave you a way to see the entire list you need.
Note that 49/8 is a little more than 6. That is the average number in this list will be just over 6. That is why the eight numbers can't all be 6 or less or all 7 or larger.

 

[smithasn]

Thank you all, I did find a SUM calculator that produced all the combination I needed, so ya its been solved, thank you all! B

 

[smithasn]

Well here goes my poor math skills: I have numbers 1,2,3,4,5,6,7,8,9,10. I want to know all the combinations of these number "including" repeating numbers that end up ( When Added Only) equal to 49. Is their a formula or online calculator that? I know of a SUM calculator but that only added them, which is what I want but I want to see variations (repeating sets) that also equal 49. I also have a requirement that I am picking sets that are only 8 digits long because that's what I want. There must be some online calculator to allow this? or show all combinations when added and then I can cull the sets. Thank you in advance for your advice!

Example straigh tset that equals 49 - from the sum calculator
10 + 9 + 8 + 7 + 6 + 5 + 3 + 1 = 49
10 + 9 + 8 + 7 + 6 + 4 + 3 + 2 = 49
-----------------------------------------
Repeating one I did by hand this cannot be all of them.
10,7,5,7,7,4,1,8 ----- these eight when added get 49
10,9,8,7,6,5,3,1 also adds up to 49

 

[Steven G]

Why did you bother finding a sum calculator when you were given one in post #3?

 

[smithasn]

Why did you bother finding a sum calculator when you were given one in post #3?

That sum calc did not allow the option to select show combo of repeating numbers combinations . It just shows adding in linear fashion maybe im wrong but???

 

[BigBeachBanana]

That sum calc did not allow the option to select show combo of repeating numbers combinations . It just shows adding in linear fashion maybe im wrong but???

If you know how to render Python code, try this.

from itertools import combinations_with_replacement

def find_combinations(candidates, target, combo_len):
    # Get all the combinations of the candidates with replacement
    # (i.e. repetition of candidates is allowed)
    combs = combinations_with_replacement(candidates, combo_len)
    # Filter the combinations to only keep those that add up to the target sum
    return ([comb for comb in combs if sum(comb) == target])

candidates = list(range(1,13))
target = 49
comb_len = 8

answer = find_combinations(candidates,target,comb_len )

Here are a few lines of the output:

[(1, 1, 1, 1, 9, 12, 12, 12),
 (1, 1, 1, 1, 10, 11, 12, 12),
 (1, 1, 1, 1, 11, 11, 11, 12),
 (1, 1, 1, 2, 8, 12, 12, 12),
 (1, 1, 1, 2, 9, 11, 12, 12),
 (1, 1, 1, 2, 10, 10, 12, 12),
 (1, 1, 1, 2, 10, 11, 11, 12),...]

print(len(answer))
[Output]: 2358 #Total number of combinations

 

[smithasn]

If you know how to render Python code, try this.

from itertools import combinations_with_replacement

def find_combinations(candidates, target, combo_len):
    # Get all the combinations of the candidates with replacement
    # (i.e. repetition of candidates is allowed)
    combs = combinations_with_replacement(candidates, combo_len)
    # Filter the combinations to only keep those that add up to the target sum
    return ([comb for comb in combs if sum(comb) == target])

candidates = list(range(1,13))
target = 49
comb_len = 8

answer = find_combinations(candidates,target,comb_len )

Here are a few lines of the output:

[(1, 1, 1, 1, 9, 12, 12, 12),
 (1, 1, 1, 1, 10, 11, 12, 12),
 (1, 1, 1, 1, 11, 11, 11, 12),
 (1, 1, 1, 2, 8, 12, 12, 12),
 (1, 1, 1, 2, 9, 11, 12, 12),
 (1, 1, 1, 2, 10, 10, 12, 12),
 (1, 1, 1, 2, 10, 11, 11, 12),...]

print(len(answer))
[Output]: 2358 #Total number of combinations

Thank you that does it!